The problem is definitely that you don't have rights to view alerts from the 2nd department. You'll need to have the administrator of that department (if it is not you) add the view alerts right to your user account.
Users are people that can log into the website, devices are things that receive alerts. By default (I think) auto create users is turned on. It's an agency setting. In which case if someone enters their email address at the log in screen and that email address matches the email listed in one of your devices it will automatically create a user account for that person and let them sign into the website. They won't have any rights to do anything except maybe manage their device, I'm not even sure they can that though.
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